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her death. That is all. I wondered whether we could find anything in her past life which might throw light on the mystery.’
    ‘What evidence have you in support of your conclusions, apart from what we discussed yesterday morning?’ asked Alastair.
    ‘Plenty of evidence,’ answered Carstairs. ‘Enough, at any rate, to satisfy myself that matters cannot be left as they are.’
    ‘Then,’ said Alastair Bing determinedly, ‘the best thing you can do is to lay your suspicions before the police. It is your duty as a citizen to invoke the aid of the law if you think that suspicious circumstances surround the death of my guest.’
    ‘I am not at all anxious to call in the police,’ Carstairs replied mildly. ‘And I’ll tell you why.’
    He held up a protesting hand to stay the flood of words which the choleric Bing seemed about to pour upon his ears, and continued gravely:
    ‘I believe that Mountjoy was murdered. I believesomeone in this house killed her. And, what is more, I believe I know now who the murderer is!’
    While Alastair Bing, bereft of speech for once, gazed helplessly at him, Mrs Lestrange Bradley slipped quietly from the room.

Chapter Six
The Key to the Mystery
    ‘INFORM THE POLICE, of course, if you think it well to do so,’ Carstairs went on. ‘I must say that to shift the responsibility of my knowledge on to the shoulders best trained to bear it would relieve me not a little. But be warned by me, and do not call in the police hastily.’
    ‘What do you know?’ cried Alastair Bing hoarsely. Carstairs shook his head.
    ‘I prefer not to say. You know as much about this affair as I do, and all that I have deduced, you also may deduce, if you care to do so.’
    ‘Oh, you mean that you don’t really know anything,’ observed Alastair Bing, looking relieved.
    ‘Bing,’ said Carstairs, ‘I don’t know anything more about this case than you knew about the Roman villa where you found that piece of broken tessellated pavement last summer. Do you remember? And yet, I recollect that you reconstructed that villa verycreditably, and wrote a learned and lengthy treatise on the subject, with, I repeat, no more data than those few tiles you found. Am I right?’
    Alastair’s face brightened.
    ‘I was personally complimented by Bethermeyr himself,’ said he triumphantly. ‘He was most enthusiastic.’
    ‘And rightly so, I feel sure,’ said Carstairs warmly. ‘Well, but you see my point, don’t you?’
    ‘No,’ snapped Bing, in his courteous way.
    ‘It is this. I have found my few tiles also. They are, in this case, the open window; the unlocked door; the disappearing stool; the stool which re-appeared, but in the wrong bathroom; the rightful stool, which had been soiled and was afterwards cleaned with turpentine that its evidence might be rendered void, and last, but not least, the little pot of dark green paint which someone kicked over on the balcony. Didn’t you notice the stain when we were up there this morning? Then, of course, there is——’
    ‘The missing watch,’ said Mrs Bradley, re-appearing with the suddenness of the Cheshire cat and with much the same sort of grin on her face.
    ‘What?’ cried Carstairs, surprised into forgetting the rest of the sentence.
    ‘Missing watch? What missing watch? I didn’t know anybody had lost a watch. Why wasn’t I told?’ said Alastair Bing.
    Mrs Bradley’s evil grin changed to an expression of innocent gravity.
    ‘Only my little joke,’ she informed them calmly.‘Well, Mr Bing, have you said anything exciting or amusing whilst I have been absent?’
    ‘I am going to call in the police,’ snapped Alastair. ‘That’s what I said, and that’s what I intend to do. I’ll send for them at once. I refuse to have my house turned into a Sherlock Holmes’ paradise.’
    So saying, he went out, slamming the door behind him.
    Immediately he had gone, Mrs Bradley delved into a capacious skirt-pocket, the flap of which was usually concealed